Expressions and formulae

Expressions and Formulae

Understanding Expressions

  • An expression is a mathematical phrase that combines numbers, variables and operations. Examples of expressions include 5x+3, 2a-7, 4b^3.
  • There are no equals signs (=) in an expression, so you can’t solve an expression in the same way you can solve an equation.
  • An expression can be simplified by carrying out the operations, this often involves collecting like terms (i.e., terms with the same variable to the same power).

Simplifying Expressions

  • Simplifying an expression means to carry out all possible operations without changing the value of the expression.
  • Simplifying often involves the use of addition and subtraction rules, as well as the distributive property.
  • Like terms consists of variables and exponents that are the same. They can be combined using the rules of addition or subtraction.
  • For example, the expression 5x + 7x - 2y can be simplified to 12x - 2y.

Forming Expressions

  • Expressions can be formed from real-world situations.
  • It involves identifying the variable quantities, deciding on the variable letters and constructing the expression.
  • For example, if a car travels at a speed of n mph for t hours then the distance travelled could be expressed as nt.

Understanding Formulae

  • A formula is a type of equation that shows the relationship between different variables.
  • The formula can specify how to calculate a quantity given certain parameters: for example, the area of a circle = πr^2 where r is the radius of the circle.
  • Formulae can be used to solve problem; to use a formula, substitute the known values of the variables into the formula to find the unknown value.

Rearranging Formulae

  • Rearranging a formula involves rearranging the equation to make a different variable the subject.
  • This often requires manipulating terms using addition, subtraction, multiplication, division, or even root functions.
  • For example, in the formula for the area of a circle, if the area (A) is known and we want to find the radius (r), the formula can be rearranged to r = √(A/π).